an:00528652
Zbl 0795.62036
H??rdle, W.; Mammen, E.
Comparing nonparametric versus parametric regression fits
EN
Ann. Stat. 21, No. 4, 1926-1947 (1993).
00017413
1993
j
62G07 62G09 62G20 62F99
kernel estimators; bootstrap; goodness-of-fit-test; integrated squared deviation; curve estimate; wild bootstrap; Monte Carlo; Engel curves
The authors consider the problem to test the parametric model \(\{m_ \theta\); \(\theta\in\Theta\}\) against the nonparametric alternative that only assumes \(m(\cdot)\) is `smooth'. They propose to use as a test statistics the integrated squared deviation of the parametric and nonparametric curve estimate. They show that the standard way of bootstrapping this statistics fails, however, wild bootstrap works. The validity of the asymptotic results is checked in a Monte Carlo experiment and on the fitting Engel curves in the mean expediture curve of a certain food.
M.Hu??kova (Praha)